Hi Stephan, I think we can get a rather good approximation of a tree
by saying the following:
hasChild is a subproperty of hasOffSpring
hasOffSpring is transitive
every offSpring of the root node (i.e., an indiviual called root) has
at most one incoming hasChild edge
(you can also say this for everything in the universe - but that would
be a bit strong)
if a node has no incoming hasChild edge, then it is the root node
...now, if you want a (strict) binary tree you need to add further
cardinality restrictions on outgoing hasChild edges.
Cheers, Uli
On 31 May 2012, at 09:40, Stephan Opfer wrote:
> Hello,
>
> I recently noticed, that although the model of an owl axiom should
> have
> tree property, it is not possible to describe a tree data structure in
> OWL. The way I would model it, is to create a class Node and a
> property
> hasChild and make the hasChild property transitive and irreflexive,
> which is not allowed in OWL-DL, because transitive properties are no
> simple properties.
>
> I searched a bit on w3c websites and their citations and also made
> another post on the protege-owl mailing
> list:protege-ontology-editor-knowledge-acquisition-system.
> 136.n4.nabble.com/Tree-Paradox-of-OWL-td4655163.html
> Someone told me, that I should post this question here, too.
>
> You don't have to read the other post. Here is a summary of my
> observations and the resulting question to this mailing list.
>
> On website [0] the restriction about composite object properties are
> described and [1] is cited for given the reason for these
> restrictions.
> However, [1] states about irreflexivity combined with transitivity:
>
> "For SROIQ and the remaining restrictions to simple roles in concept
> expressions as well as role assertions, it is part of future work to
> determine which of these restrictions to simple roles is strictly
> necessary in order to preserve decidability or practicability. This
> restriction, however, allows a rather smooth integration of the new
> constructs into existing algorithms."
>
> So my question is: Has someone proven, that the restrictions about
> transitivity and irreflexivity can be loosen? Otherwise, OWL cannot
> describe a tree data structure on "schema level".
>
> Best Regards,
> Stephan
>
> [0] http://www.w3.org/TR/owl2-syntax/#The_Restrictions_on_the_Axiom_Closure
>
> [1] http://www.cs.man.ac.uk/~sattler/publications/sroiq-TR.pdf
>
>